arXiv:1102.3916v1 [astro-ph.GA] 18 Feb 2011
The Gradients in the 47 Tuc Red Giant Branch Bump and
Horizontal Branch are Consistent With a Centrally-Concentrated,
Helium-Enriched Second Stellar Generation
D. M. Nataf1, A. Gould1, M.H. Pinsonneault1, P.B. Stetson2
We combine ground and space-based photometry of the Galactic globular
cluster 47 Tuc to measure four independent lines of evidence for a helium gra-
dient in the cluster, whereby stars in the cluster outskirts would have a lower
initial helium abundance than stars in and near the cluster core. First and sec-
ond, we show that the red giant branch bump (RGBB) stars exhibit gradients in
their number counts and brightness. With increased separation from the cluster
center, they become more numerous relative to the other red giant (RG) stars.
They also become fainter. For our third and fourth lines of evidence, we show
that the horizontal branch (HB) of the cluster becomes both fainter and redder
for sightlines farther from the cluster center. These four results are respectively
detected at the 2.3σ, 3.6σ, 7.7σ and 4.1σ levels. Each of these independent lines
of evidence is found to be significant in the cluster-outskirts; closer in, the data
are more compatible with uniform mixing. Our radial profile is qualitatively
consistent with but quantitatively tighter than previous results based on CN ab-
sorption. These observations are qualitatively consistent with a scenario wherein
a second generation of stars with modestly enhanced helium and CNO abundance
formed deep within the gravitational potential of a cluster of previous generation
stars having more canonical abundances.
Subject headings: stars: evolution – globular clusters: individual: 47 Tuc.
1Department of Astronomy, Ohio State University, 140 W. 18th Ave., Columbus, OH 43210
2Herzberg Institute of Astrophysics, National Research Council Canada, 5071 West Saanich Road, Vic-
toria, BC V9E 2E7
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47 Tuc (NGC 104) is among the most massive globular clusters in the Galaxy and is
thus one of the most powerful laboratories to investigate the finer details of globular cluster
formation and evolution. As the large stellar population renders any potential statistic more
accessible, it is interesting that 47 Tuc is not among those globular clusters with more clearly
delineated evidence for multiple populations (Bergbusch & Stetson 2009).
However, it has been known for several decades that the stars in the inner part of
the globular cluster have stronger CN absorption (Norris & Freeman 1979; Paltoglou 1990).
Recently, di Criscienzo et al. (2010) have argued that this chemical gradient is due to the
presence of multiple generations of stars, with later generations being helium and CN en-
hanced by the ejecta of first-generation asymptotic giant branch (AGB) stars. They found
strong evidence of a helium-spread in the morphology of the subgiant branch (SGB) and hor-
izontal branch (HB) stars. Their work followed an investigation by Anderson et al. (2009),
who used Hubble Space Telescope (HST) data to measured the color widths of the cluster
main sequence, which they argued could be explained by a spread of ∆Y ∼ 0.027. If the
helium-enhancement is due to a second generation, and if the second generation is indeed
more centrally concentrated, as suggested by the CN band strengths and dynamical argu-
ments (D’Ercole et al. 2008), one should expect a higher helium abundance in the center.
It has recently been posited that the presence of multiple generations differing in properties
such as initial helium abundance and the relative abundances of sodium and oxygen are in
fact a ubiquitous property of globular clusters (Carretta et al. 2010).
In this paper we test the hypothesis of a helium gradient in 47 Tuc using four methods
that are rooted in the properties of two densely-populated phases of post main-sequence
stellar evolution, the red giant branch bump (RGBB) and the HB. The RGBB phase occurs
during the first ascent of the red giant branch. As the hydrogen burning shell expands, it
eventually comes into contact with the convective envelope (Cassisi & Salaris 1997). This
increase in fuel causes the star to become fainter as the fuel is used up before becoming
brighter again, effectively crossing the same luminosity three times, leading to a “bump”
in the luminosity function. This bump is most populated and thus more measurable in
metal-rich clusters such as 47 Tuc (Zoccali et al. 1999; Bono et al. 2001; Riello et al. 2003;
Di Cecco et al. 2010; Cassisi et al. 2011).
Stellar evolution predicts the RGBB lifetime to be significantly shortened for increased
initial helium abundance (Bono et al. 2001; Di Cecco et al. 2010; Nataf et al. 2010). If this
stellar theory prediction is correct, and the hypothesis of a centrally-concentrated, helium-
enhanced population in 47 Tuc is correct as well, then RGBB stars should be less prominent
relative to the remaining RG stars closer to the cluster center. We detect a variation in the
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equivalent width (EW) of the RGBB at the ∼2.3σ level. For our second test, we also show
that the RGBB stars are fainter with increasing distance from the cluster center, a detection
made at the ∼3.6σ level.
We also investigate the cluster HB stars. We show that the HB stars are both fainter
(∼7.7σ) and redder (∼4.1σ) farther from the cluster center, though the gradient levels off
in the inner ∼200′′. This is the expected trend for increased helium in stellar models, as
seen for example in Figure 1 of di Criscienzo et al. (2010), which was produced using the
code ATON 2.0 (Ventura et al. 1998; Ventura & D’Antona 2009). This gradient is already
known from Briley (1997), who showed with high confidence that HB stars with strong CN
absorption were ∼0.04 mag brighter. They argued that this effect could be explained by
either a small difference in the core mass of helium burning stars or a small difference in the
initial helium abundance of those brighter, CN-enhanced HB stars.
We have conducted these experiments by combining two independent datasets, a space-
based dataset toward the cluster center (Sarajedini et al. 2007) and a comprehensive ground-
based dataset for the remaining sightlines (Stetson 2000). The latter contains ∼60% of the
stellar sub-populations studied in this paper. The two datasets respectively include ∼500
and ∼700 HB stars, as well as ∼120 and ∼150 RGBB stars. For all four tests, we find
significant detections of the trends expected from a helium gradient in the cluster outskirts,
with no discernible trend within the cluster center. This is most consistent with a picture of
two stellar generations that are evenly mixed within the cluster center, but with the second
generation having a characteristic radius beyond which its numbers fall more rapidly. Our
estimated transition radius of a few arcminutes is smaller than that derived from previous
investigations of CN absorption among cluster giants. Briley (1997) found that the ratio of
CN-strong to CN-weak stars was approximately constant up to ∼10-15 arcminute separations
from the cluster center, beyond which the ratio fell rapidly.
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Fig. 1.— The field of view (FOV) of observations used in this work. Point sources from the
ground based photometry are shown as points. The inner parallelogram centered at (RA,
DEC)∼(6.023, -72.081) or (α,δ) = (00 : 24 : 06,−72 : 04 : 52) corresponds to the FOV of
the HST dataset.
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Fig. 2.— LEFT: The color-magnitude diagram of the HST dataset. The RG branch (in-
cluding the RGBB), the HB, and the SGB are all contained within their respective color-
magnitude selection boxes. RIGHT: Magnitude distribution of RG stars. The RGBB stands
out as a prominent and significant peak at V = 14.51.
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Fig. 3.— Same as in Figure 2 but for the ground based data rather than the ACS data. The
RGBB peak is detected at V = 14.54. The difference of 0.03 mag with that found in the
space-based dataset is very possibly due to differences in convention.
We make use of two different data sets in this study to maximize the available informa-
tion and constrain the effect of any possible systematics.
For the cluster center, we use photometry obtained with HST’s Advanced Camera for
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Surveys (ACS) (Sarajedini et al. 2007). The data were taken as part of an HST treasury
program to obtain high signal-to-noise ratio photometry down the to the lower main sequence
for a large number of Galactic globular clusters. We use Vgroundand Iground(hereafter “V ” and
“I”) photometry, which were transformed from the original F606W and F814W photometry.
Artificial star tests demonstrate that the photometry is expected to be very precise and
complete at the brightness of the RGBB (Anderson et al. 2008).
We also use U, B, V , and I observations that come from a database of original and
archival observations (Stetson 2000), which are calibrated on the Landolt (1992) photometric
system. These observations and the general properties of the 47 Tuc color-magnitude dia-
gram (CMD) are described in Bergbusch & Stetson (2009). We make use of stars in these
observations that are outside of the coordinate range observed by the ACS dataset. The 135
point sources that are located within 30′′of (α,δ) =(00:21:30.3 −71:56:03), corresponding
to the location of Bologna A (Bellazzini et al. 2005), are not included in our analysis. This
does not affect our analysis as the background population is way outside the cluster center
and its spatial extent is only 60′′. We show the respective fields of view in Figure 1. CMDs
for the space-based and ground-based are respectively shown in Figures 2 and 3.
3. Stellar Evolution Models
We use the Yale Rotating Evolution Code (Delahaye et al. 2010) to compare our out-
put parameters to theory for the RG and RGBB populations. Theoretical considerations
for the HB population are taken from the literature (Renzini 1994; Ventura et al. 1998;
Girardi & Salaris 2001; Ventura & D’Antona 2009; di Criscienzo et al. 2010).
At the expected metallicity ([M/H]∼ −0.50) and age (∼12 Gyr) of 47 Tuc (McWilliam & Bernstein
2008; Carretta et al. 2010), we find that every 1% increase in the initial helium abundance
by total stellar mass yields a ∼10% decrease in the lifetime of the RGBB, corresponding to a
decrease of ∼0.02 mag in the EW. Two representative models are shown in Figure 4. Within
the models, we compute the EW of the RGBB by multiplying the lifetime of the RGBB by
the average of the two slopes of magnitude versus time before and after the RGBB. The
predicted stellar properties of the RGBB as a function of initial composition are summarized
in Table 1. We note the helium-rich track has a higher initial [M/H] only because it has
a lower initial hydrogen abundance – the initial metallicity content by mass are the same.
We also introduce the notation δVRGBBto refer to the difference in magnitudes between the
brightest and faintest parts of the RGBB phase as predicted by stellar models.
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Fig. 4.— Two representative stellar tracks for a 12 Gyr population with a metallicity [M/H]≈
−0.50. Model points with a luminosity corresponding to the RGBB phase are plotted in blue,
and the underlying red giant branch in red. TOP: Primordial helium content Y= 0.25, the
EW of the RGBB is 0.33 mag. BOTTOM: Primordial helium content Y= 0.28, the EW
of the RGBB is 0.28 mag. The EW is computed by multiplying the lifetime of the RGBB
phase, shown by the length of the black horizontal line, by the average of the slopes of the
luminosity evolution function just outside the RGBB, which are shown in green.
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Table 1: Predicted Stellar Properties of the RGBB
–Model AModel B
Age at RGBB
Median RGBB brightness
Teffat RGBB median brightness
Luminosity Evolution before RGBB
Luminosity Evolution after RGBB
16.71 mag Gyr−1
23.65 mag Gyr−1
17.99 mag Gyr−1
26.11 mag Gyr−1
4.Red Giant Branch Bump Gradients in Brightness and Number Counts
We show that the RGBB grows both fainter and more numerous relative to the RG stars
with increased separation from the cluster center, and that the trends are both statistically
significant. None of these trends are detected with significance in the inner ∼100′′of the
cluster as traced by the space-based dataset, consistent with previous work (Briley 1997)
and our measurements of the HB (discussed in a Section 5) that the two stellar populations
are smoothly mixed in and near the cluster center.
4.1. Fitting for the RGBB
In both datasets, we cut out a parallelogram around the red giant branch that keeps
stars no more than 1.0 mag brighter nor 1.6 mag fainter than the RGBB in V . The range in
magnitude is chosen to be as wide as possible while still excluding the HB and AGB stars.
We show our color-magnitude cuts for the space-based and ground-based data in Figures 2
and 3, respectively.
We fit for the RGBB and the RG using a combination of an exponential for the mag-
nitude distribution of RG stars (equivalent to a power-law distribution in luminosity) and a
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Gaussian for the RGBB:
N(m) = Aexp
B(V − VRGBB)
−(V − VRGBB)2
N(m) = A
B(V − VRGBB)
−(V − VRGBB)2
where VRGBB is the peak magnitude of the RGBB, σ is the dispersion, N is the number
of RGBB stars, and A and B are the normalization and scale of the exponential. As in
Nataf et al. (2010), we define the equivalent width of the RGBB, EW, to be the ratio of the
number of RGBB stars to the number density of RG stars at the magnitude of the RGBB. In
this parametrization EW = N/A. We use Markov Chain Monte Carlo (MCMC) to obtain
the maximum likelihood values for the parameters. For each value of the parameters tested
by the MCMC, we compute the log-likelihood ℓ:
where Nobsis the total number of stars, and the parameter A is selected in each run of the
MCMC such that the integral of the function N(m) over the magnitude range is equal to
Nobs. We do not fit an RGBB model to the data by first binning it, but it can be shown that
this method is equivalent to binning data in the limit of infinitesimal bin widths.
4.2. Decreased Brightness and Increased Equivalent Width for RGBB Stars
Farther From the Cluster Core
Fitting for gradients in the brightness of the RGBB VRGBB and the number counts
parameter EW with separation from the cluster center yields statistically significant im-
provements in the fit for the ground-based dataset, with no significant improvement in the
space-based dataset toward the cluster core.
We fit for a gradient using the following extension to our parametrization:
log(r) − log(r)
EW = EW0+
log(r) − log(r)
where r = (Ri−RCC) is the separation in arcseconds of the location of the ith star, Rifrom
the cluster center RCC, taken here as being (α,δ) = (00:24:05.4, −72:04:53), and is taken
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from Vizier (Ochsenbein et al. 2000). The mean of the logarithmic separation for all the
RG+RGBB stars used to construct the fit is designated log(r). We tested parametrizations
of both separation, squared separation and the log of separation and found that using the
logarithmic separation from the cluster center yielded the largest improvement in the fit as
measured by ∆ℓ.
Allowing gradients for both VRGBBand EW yields dVRGBB/dlog(r) = (0.083 ± 0.023)
mag dex−1, and dEW/dlog(r) = (0.27 ± 0.12) mag dex−1. These two gradients each retain
nearly identical values when the other is fixed to being zero and can therefore be considered
independent. Both gradients go in the direction expected from stellar theory in the presence
of a helium gradient. The model predictions shown in Figure 4 predict that for a 12 Gyr
population with a metallicity [M/H]≈ −0.50, the brightness should increase by ∼0.05 and
the EW should decrease by ∼0.07 mag and as the initial helium abundance is increased from
Y=0.25 to Y=0.28. Since the total span of the ground-based dataset in arcseconds is approx-
imately 1 dex, the measured gradients are a little higher than the theoretical expectations.
A graphical representation of these gradients is shown in Figure 5
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Fig. 5.— The RG+RGBB stellar population of the groundbased dataset is split up into three
equal subpopulations, sorted by radial separation from the center of the cluster. The trends
expected in the presence of a helium gradient, that of increasing EW and declining brightness,
are both observed. We have fixed the exponential slope of the power law to B = 0.76, as is
obtained when fitting to the entire cluster. This does not affect the parameter VRGBBbut it
does slightly reduce the trend in EW. Vertical lines are drawn in each panel corresponding
to the peaks of the inner and outer RGBB peaks, at V = 14.50 and V = 14.56.
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5.Horizontal Branch Gradients in Color and Brightness
The trends in color and brightness with respect to the distance to the cluster center for
HB stars are compatible with an even mixing of the two stellar generations in the cluster
center and with the helium-enhanced second generation decreasing more rapidly at larger
radii. We discuss four possible contaminating effects and find that none of them have the
same predicted trends as are observed.
As there is no definitive way to cleanly and completely separate horizontal branch stars
from background contamination stars and AGB stars, we utilize visually satisfactory color-
magnitude boxes in the space-based and ground-based datasets, respectively shown in Fig-
ures 2 and 3. In the space-based data, we tabulate 545 stars with 0.82 < (V − I) < 0.98
and 13.8 < V < 14.2, whereas in the ground-based dataset we tabulate 771 stars with
0.7 < (B − V ) < 0.9 and 13.8 < V < 14.2. For both datasets, we compute the correlation
between brightness and the log of the separation from the cluster center.
In the ground-based data, the HB stars become fainter and redder with increased sep-
aration from the cluster center. The brightness gradient is (0.072 ± 0.009) mag dex−1in V ,
and the color gradient is (0.021±0.005) mag dex−1in (B−V ). Using only those sources that
have at least 5 measurements in each filter, we also obtain color gradients of (0.064±0.009)
mag dex−1in (B − I) and (0.078 ± 0.013) mag dex−1in (U − V ). The gradients go in the
same direction as expected if a helium-enriched, second generation of GC cluster exists in
47 Tuc with a more central concentration. The HB stars in the space-based dataset, toward
the cluster center, has a slight trend of getting redder with increased separation from the
cluster center, but it is a very weak trend, 1.3σ, and is without a corresponding trend in
We show the colors and brightness for HB stars as a function of separation from the
cluster center in Figure 6. The profile is one of even mixing between the two populations
within the inner ∼200′′, with the brighter HB stars falling off in relative numbers between
∼200 and ∼400′′. That the color and brightness profiles show the same structure with respect
to separation from the cluster center is evidence that the trends are genuine attributes of
the cluster stars rather than statistical fluctuations.
The potential contamination effects in this comparison would not go in the same direc-
tion as the measured gradient. First, both signals go in the opposite direction to the weak
signal expected from the known CNO variation in the cluster. As stars in the cluster center
have higher CNO, they ought to be slightly (∼0.01 mag) redder and fainter with decreased
distance to the cluster center. We refer the reader to Figure 1 of di Criscienzo et al. (2010).
Second, this result cannot be explained by having the second population be substantially
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younger. A younger HB population at this metallicity would indeed be brighter, but it
would also be redder rather than bluer (Girardi & Salaris 2001). A third possible effect is
that of binary interactions. Stars closer to the cluster center will be more likely to have
a binary companion (Sollima et al. 2007; Hurley et al. 2007), which implies increased mass
loss during the red giant branch. That would make HB stars bluer with decreasing distance
to the cluster center as we observe, but it would also make them fainter. In their recent
dynamical investigation of the cluster, Giersz & Heggie (2010) found that the fraction of
stars in binary pairs should level off after a ∼100′′separation from the cluster center. Hence,
if binary interactions were the cause of this effect they would induce a much tighter radial
profile. Lastly, the fact that each of the color gradients is ∼3× larger than that detected for
the RG stars at the level of the RGBB (discussed in section 6) contradicts the hypothesis
that the HB gradients would be due to a reddening or blending gradient.
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Fig. 6.— Color and brightness of the HB stars binned as a function of separation from the
cluster center. Left-hand panels show the data for the cluster-core and right-hand panels
for the rest of the cluster. Top panels show the color of the HB star, and bottom panels
show the brightness in V . The thick black points are the means and the error bars are the
standard error in the mean for subsamples of ∼70 HB stars binned in separation from the
cluster center. The more numerous, less sharp points correspond to individual HB stars.
6.Note Regarding a Small Color Gradient on the Red Giant Branch
We find evidence for a small color gradient in the cluster RG stars that is not a predicted
outcome of the models in the presence of a helium gradient. We compute the least-squares
relation between the measured colors of all the RG+RGBB stars and their separation from